Where are the second- (and third-)generation proofs of the classification of finite simple groups up to?

2012-11-29T23:59:00Z

According the the Wikipedia page, the second generation proof is up to at least nine volumes: six by Gorenstein, Lyons and Solomon dated 1994-2005, two covering the quasithin business by Aschbacher and Smith in 2004, and one by Aschbacher, Lyons, Smith and Solomon in 2011. However, this latter book is really just the second part of an outline of the proof, the first part of which was written by Gorenstein in the 80s (the reason for the delay is, of course, that the quasithin case hadn't actually been settled at the time of the announcement of completion). Hence the last update on the second-generation proof is really 2005.

With the recent formal proof in Coq of the Odd-order Theorem, it would be good to know where the traditional proof is up to.

Answer by Nick Gill for Where are the second- (and third-)generation proofs of the classification of finite simple groups up to?

2012-11-30T13:55:58Z

With respect to the second generation proof you can get an answer `from the horse's mouth' if you like: Ron Solomon gave an update on the program at BIRS recently and a video of his talk is here.

He starts the talk by comparing its progress to `the receding of the glaciers'! In reality, though, they've made very significant headway into the later volumes. (In particular he mentions, around 9:30, that volume 7 is in preparation, and it is mainly this volume that he's discussing in the talk.)

Where are the second- (and third-)generation proofs of the classification of finite simple groups up to? - MathOverflow

Where are the second- (and third-)generation proofs of the classification of finite simple groups up to?

Answer by Nick Gill for Where are the second- (and third-)generation proofs of the classification of finite simple groups up to?